When an addon grows it becomes convenient to break it out into modules, do those other modules (
.py files) also need a license block or is it sufficient to only put it in the
No, but it's good practice. All the official Blender addon files have a license block.
Some projects uses
See COPYING for license in all their files, instead of full license block (and include a file thus named), but generally they put some information about license in all component source files.